Question

.
6. A wire is bent to form a circle of radius 7 cm. If this wire is reshaped to form a square,
find the:
(a) side of the square.
(b) area of the square.
​

Answer 1

Step-by-step explanation:

side of square = 11 cm

area of square = 121 cm²

Answer 2

Given:

• Radius of the circle = 7 cm
• The same wire is bent and reshaped to form a square.

To find:

• Side of the square.
• Area of the square.

Solution:

As the wire is bent to form a square, it means that circumference of the circle is equal to the perimeter of the square.

We know that,

$\boxed {\mathfrak {\green {Circumference\ of\ circle = 2 \pi r}}}$

Substitute the values,

Circumference = 2×$\sf \dfrac {22}{7}$ × 7

☆ 7 will be canceled out.

Circumference = 2×22

$\boxed {\bf {\orange {Circumference\ of\ circle = 44\ cm}}}$

Now,

Perimeter of square = 44 cm

We know that,

$\boxed {\mathfrak {\pink {Perimeter\ of\ square = 4s}}}$

Substitute the values,

44 = 4s

$\sf \dfrac {44}{4} = s$

$\boxed {\bf {\red {Side\ of\ square = 11\ cm}}}$

Now,

We know that,

$\boxed {\mathfrak {\blue {Area\ of\ square = s^{2}}}}$

Substitute the values,

Area = (11)²

$\boxed {\bf {\gray {Area\ of\ square = 121\ cm^{2}}}}$

Final answer:

• Side of the square is 11 cm.
• Area of the square is 121 cm².